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Properties

Label 266910i
Number of curves $2$
Conductor $266910$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 266910i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
266910.i2 266910i1 \([1, 1, 0, -2452, 141916]\) \(-1631405145996361/7882185937500\) \(-7882185937500\) \([2]\) \(761856\) \(1.1592\) \(\Gamma_0(N)\)-optimal
266910.i1 266910i2 \([1, 1, 0, -58702, 5440666]\) \(22371441369258096361/43635080711250\) \(43635080711250\) \([2]\) \(1523712\) \(1.5057\)  

Rank

sage: E.rank()
 

The elliptic curves in class 266910i have rank \(2\).

Complex multiplication

The elliptic curves in class 266910i do not have complex multiplication.

Modular form 266910.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} + 2 q^{13} + q^{14} - q^{15} + q^{16} + 2 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.